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At the early iteratives, the mutation rate is bigger and the aim is to make particles to explore smaller and isolate region and to avoid the algorithm trapping to the local optimum. While the algorithm runs, the mutation rate will be decreased to reduce the disturbing to the particles. IPSO adopts a new method that congregates some neighboring individuals to form multiple sub-populations in order to lead particles to explore new search space. Additionally, our algorithm incorporates a mechanism with a simple and easy penalty function based on the largest distance between the particle and the boundary of the feasible region to handle constraint.

IPSO采用了一种新型的变异策略，变异概率随着算法的运行是动态变化的：在算法运行初期，变异概率大，其目的是使算法不但能够探测到目标空间中的孤立区域，而且避免搜索陷入局部极值；在算法运行后期，变异概率逐渐变小，以减少对粒子的扰动；算法通过将部分具有邻近距离的粒子聚集成核形成多子群引导种群中粒子的飞行；采用一个简单的基于粒子与可行域边界最远距离的罚函数处理约束的机制，使得算法高效实现。

This class of process had no close form of probability density function and finite second order moment.

与其他统计模型不同，α-稳定分布没有统一闭式的概率密度函数，其二阶及二阶以上统计量均不存在。

This class of process has no close form of probability density function and finite second order moments.

与其它统计模型不同，α稳定分布没有统一闭式的概率密度函数，其二阶及二阶以上统计量均不存在。

The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived.

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究，采用将矩形域函数表示为复高斯函数叠加的技巧，推导出了解析的传输公式，在特殊情况下，该公式简化为在无光阑情况下的传输公式。

This is necessary as we too must become vegetarian in order to transcend our own fission thought-form within.

这是必要的，因为我们也必须变成素食者，以达到超越我们内在核裂变的思想形态的目的。

In order to design and operate an activated sludge wastewater treatment system efficiently, it is necessary to understand the role of the microorganisms to decompose the organic waste and to form a satisfactory floc, which is a prerequisite for the effective separation of the biological solids in the settler.

为了设计并运作一个活性污泥污水处理系统的效率，是要了解作用的微生物分解有机废弃物，组成一个令人满意絮，这是一个先决条件，有效地分离生物颗粒的定居。

In order to foreshadow the type of presentation required for computer use, data will be prepared in tabular form

为了显示一下使用计算机所需的表示方式，其中数据用表格形式列出。

First, we should do exercises everyday in order to form into a good habit.

第一，我们应该每天锻炼，这样能形成一个良好的习惯。

You should form a habit to arrange your things in order.

你应当养成习惯把你的东西整理好。

In order for the baby to eat the things he does not love, it is necessary to use his form can not choose to feed, or the food crumble on the porridge, the煎包dishes or make soft egg rolls.

为了让婴儿吃他不爱吃的东西，就必须用他无法选择的形式来喂，或者把食物弄碎放在粥里，或者做成软煎包菜蛋卷。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐